Mother–child communication about relative proximity to a landmark: What role does prototypicality play?

Journal of Experimental Child Psychology 178 (2019) 41–59

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Mother–child communication about relative proximity to a landmark: What role does prototypicality play? Megan G. Lorenz, Jodie M. Plumert Department of Psychological and Brain Sciences, University of Iowa, Iowa City, IA 52242, USA

a r t i c l e

i n f o

Article history: Received 31 January 2018 Revised 3 September 2018

Keywords: Relative proximity Reference frames Spatial communication Prototypicality Dimensional adjectives Parent-child communication

a b s t r a c t This investigation examined how prototypicality affects mother– child communication about relative proximity. In the first two experiments, mothers of 2.5-, 3.0-, and 3.5-year-old children verbally disambiguated a target hiding container from an identical non-target hiding container when the two containers were placed at a smaller (more prototypical) or larger (less prototypical) distance from a landmark. Children then searched for the hidden object. When the absolute distance was smaller, mothers used more consistent frames of reference in their directions and even 2.5-year-olds largely followed those directions successfully. When the absolute distance was larger, mothers used multiple reference frames in their directions (a ‘‘kitchen sink” strategy) and children had more difficulty in following directions (especially 2.5-year-olds). A third experiment in which we controlled mothers’ directions confirmed that the increased absolute distance, and not the mothers’ direction-giving strategies, led to 2.5-year-olds’ impaired search performance. These results indicate that young children’s understanding of relative proximity develops from more prototypical cases (smaller distances) to less prototypical cases (larger distances) and that mothers’ attempts to compensate for young children’s difficulty with less prototypical cases did not improve their search performance. Ó 2018 Elsevier Inc. All rights reserved.

E-mail addresses: [email protected] (M.G. Lorenz), [email protected] (J.M. Plumert) https://doi.org/10.1016/j.jecp.2018.09.004 0022-0965/Ó 2018 Elsevier Inc. All rights reserved.

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Introduction Communicating about location is a common everyday activity for parents and children alike. These conversations often involve referring to the relative proximity of two or more objects to a landmark. For example, if a child wants to know which cup on the counter belongs to him or her, a parent might respond with ‘‘Yours is the one closer to the sink.” Previous work has largely focused on young children’s understanding of relative concepts such as close/far and high/low in the context of judgment tasks, where children are asked to judge the relative proximity of objects to a landmark or the relative height of objects on a vertical board (Hund & Plumert, 2007; Smith, Cooney, & McCord, 1986). Although these studies have yielded valuable information, very little is known about how young children understand relative concepts within the context of communication tasks (for an exception, see Plumert, Haggerty, Mickunas, Herzog, & Shadrick, 2012). As noted above, communication about relative proximity clearly plays an important role in real-world tasks such as giving and following directions about missing objects. Here, we examined mother–child communication about relative proximity in a task where mothers described the location of a hidden object to their young children and young children used those directions to search for the hidden object. We were particularly interested in how the absolute distance between a pair of hiding locations and a landmark affects mothers’ direction-giving about relative proximity and young children’s ability to successfully follow those directions. Relational thinking has long been considered a hallmark of higher-order cognition (Gentner, 2003; Piaget, 1928; Vygotsky, 1962). An important manifestation of such thinking is the ability to make relative comparisons of objects along one or more continuous dimensions such as size and height. These relative comparisons make it possible to describe one object as bigger, taller, or heavier than another object. Previous work on children’s understanding of dimensional adjectives such as big and little or high and low shows that young children’s understanding of such adjectives undergoes significant developmental change during early childhood (e.g., Ebeling & Gelman, 1988; Nelson & Benedict, 1974). A major part of this change is a shift from correctly applying these adjectives in a narrow set of more prototypical cases to correctly applying these adjectives in a broader range of less prototypical cases (Clark, 1970; Sera & Smith, 1987; Smith et al., 1986; Smith, Rattermann, & Sera, 1988; see also Meints, Plunkett, Harris, & Dimmock, 2002, and Sinha, Thorseng, Hayashi, & Plunkett, 1994, for similar arguments about spatial prepositions). For example, Smith et al. (1986) demonstrated that young children make consistent judgments of relative height only when the object is at a highly prototypical location. They presented 3-, 4-, and 5-year-olds with a 6-foot-tall apparatus and asked them to judge whether a single object was high or low at each 1-foot increment. The 3-year-olds primarily judged that a single object was high when at the top of the apparatus and low when at the bottom. The 4and 5-year-olds’ judgments of high and low included a broader range of heights, suggesting that older children can apply the labels high and low even when the object is some distance from one of the extreme values. In a follow-up study, Smith et al. (1988) found that individual children were more successful at judging the relative height of two objects when their previously assessed high/low classifications of a single object spanned a broader range of values. These results support the idea that young children initially view dimensional terms as describing prototypical categorical states. To what extent do young children have difficulty in judging the relative proximity of locations to a landmark when the distances are less prototypical (larger) than more prototypical (smaller)? Hund and Plumert (2007) addressed this question by examining whether the absolute distance of objects to a landmark affects young children’s judgments of relative proximity. Young children (3- and 4year-olds) and adults were asked to judge whether a set of target blocks was ‘‘by” or ‘‘not by” a central landmark. In the intervening condition another set of blocks was arranged between the set of target blocks and the landmark, whereas in the non-intervening condition another set of blocks was arranged outside of the set of target blocks. The 4-year-olds and adults were significantly more likely to judge the target blocks as ‘‘by” the landmark in the non-intervening condition than in the intervening condition, whereas the 3-year-olds’ judgments of nearby-ness did not depend on whether there

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were intervening blocks. However, a second experiment revealed that when the absolute distance between the landmark and the target blocks was smaller, 3-year-olds were more likely to judge the target blocks as ‘‘by” the landmark in the non-intervening condition than in the intervening condition. In later work, Hund and Naroleski (2008) extended these findings to a memory task, indicating that absolute distance affects young children’s memory for relative proximity as well (see also Hund, 2010). As noted earlier, comparisons of relative proximity also play an important role in communication about location. These comparisons can involve communicating about which of two objects is closer to a landmark (e.g., one glass is closer to the sink than is another glass) or which of two landmarks is closer to an object (e.g., a glass is closer to the sink than to the refrigerator). A previous study on mother–child communication about relative proximity examined how mothers give directions and how young children follow directions involving the relative proximity of a target and non-target hiding location to two landmarks (Plumert et al., 2012). Mothers of 2.5-, 3.0-, and 3.5-year-old children described the location of an object that was hidden in one of two identical canisters located on either side of a blue circle on the floor in front of the mother–child dyad. The location of the target and non-target canisters varied in their relative proximity to the mother–child dyad and the circle. Mothers overwhelmingly relied on relative proximity by pointing out whatever was closest to the target canister on a given trial (i.e., either the mother–child dyad or the circle). This suggests that mothers were sensitive to the developmental level of the child, with previous research robustly demonstrating young children’s preference for proximal landmarks over distal ones in a variety of tasks (e.g., Acredolo, 1978; Allen & Kirasic, 1988; Bullens, Klugkist, & Postma, 2011; Bushnell, McKenzie, Lawrence, & Connell, 1995; Craton, Elicker, Plumert, & Pick, 1990; Newcombe, Huttenlocher, Drummey, & Wiley, 1998; Overman, Pate, Moore, & Peuster, 1996). Children’s search success in the task was a function of age and the type of reference frame used. In particular, 2.5- and 3.0-year-olds were significantly above chance only when their mothers used person-only reference frames and the target container was relatively close to the mother–child dyad (e.g., ‘‘It’s in the one close to Mommy”), whereas 3.5-year-olds performed at levels significantly above chance in response to both person-only and circle-only reference frames. These results indicate that younger children struggle to follow directions involving relative proximity when comparing the distances between a target and non-target hiding location and two different landmarks, particularly when the landmark is not a person. An important question left unanswered by the previous research on parent–child communication about relative proximity is how parents and children respond to smaller (more prototypical) versus larger (less prototypical) distances between a pair of hiding locations and a landmark. The work by Hund and Plumert (2007) and Hund and Naroleski (2008) suggests that young children should have more difficulty in following directions disambiguating a target from a non-target hiding location when the distance between the pair of locations and a landmark is larger than when it is smaller. However, this work was carried out in the context of judgment and memory tasks. In a semi-naturalistic communication task such as that used in Plumert et al. (2012), parents might try to compensate for young children’s difficulties with following directions involving less prototypical cases of relative proximity by providing extra information in their directions. A wealth of research has demonstrated that parents tailor their guidance to the developmental level of their children (e.g., Gauvain, Fagot, Leve, & Kavanagh, 2002; Plumert & Nichols-Whitehead, 1996; Rogoff, Ellis, & Gardner, 1984; Wertsch, McNamee, McLane, & Budwig, 1980). For example, Plumert and Nichols-Whitehead (1996) asked 3- and 4-year-old children to give directions to their parents about where to find a mouse hidden in a one-room dollhouse. Within the dollhouse were several pairs of identical primary landmarks that served as hiding locations. These landmarks were always placed next to pieces of furniture that served as larger secondary landmarks. Parents were encouraged to talk with their children until they knew where the mouse was hidden. Plumert and Nichols-Whitehead found that parents provided directive prompts more often to 3-year-olds than to 4-year-olds and that they provided more directive prompts earlier than later in the experimental session. A second experiment in which the types of prompts children received after giving directions were experimentally controlled (i.e., no prompts, nondirective prompts, or directive prompts) revealed that directive prompts elicited improved directions across the session for both age groups.

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Collectively, these results reveal that parents adjust their support in response to their children’s age and level of experience with the task and that this support facilitates young children’s communication about location. The goal of the current investigation was to examine how parents and young children communicate about relative proximity in more prototypical (a smaller distance) and less prototypical (a larger distance) cases. We adapted Plumert et al.’s (2012) communication task in two ways. First, we changed the spatial configuration of the two containers and their relation to the landmark (the circle on the floor) to emphasize the relationship of the target and non-target containers to a single landmark. Plumert et al. placed the containers on opposite sides of the landmark, but we placed them on the same side of the landmark. Second, we changed the absolute distance between the containers and the landmark across experiments in order to examine how absolute distance affects direction-giving and direction-following in the task. In Experiment 1 of the current investigation and in Plumert et al. (2012), the two hiding containers were always 2 and 12 in. away from the landmark. In Experiments 2 and 3 of the current investigation, we shifted the containers so that they were always 12 and 22 in. away from the landmark. Given that Plumert et al. found significant changes in young children’s direction-following skills between 2.5 and 3.5 years of age, we studied children of the same ages in the current investigation. Mothers of 2.5-, 3.0-, and 3.5-year-old children described the location of an object that was hidden in one of two identical canisters located on the same side of a blue circle on the floor in front of the mother–child dyad. Over 16 test trials, the two containers were placed on one side of the circle for half of the trials and on the other side of the circle for the other half of the trials. The container that served as the target was counterbalanced across all trials. After mothers gave their directions, children attempted to find the object on the first try. To address how varying the absolute distance between the pair of containers and the landmark affected mothers’ direction-giving and children’s directionfollowing, we examined the reference frames and spatial terms mothers used to describe the target location and children’s success in finding the toy on the first try. Based on previous work (Hund & Naroleski, 2008; Hund & Plumert, 2007; Plumert et al., 2012), we expected children (especially the youngest age group) to have more difficulty in following directions involving relative proximity when the distances were larger than when they were smaller. We were also interested in whether mothers would try to compensate for young children’s difficulties with larger distances by providing more information in their directions and whether more information would be helpful to children. Experiment 1 Method Participants A total of 48 mother–child dyads participated, with approximately equal numbers of boys and girls in each of three child age groups. There were 16 2.5-year-olds (M = 30 months 1 day, range = 28;22– 31;9 [months;days]; 7 girls), 16 3.0-year-olds (M = 36 months 14 days, range = 35;18–37;11; 8 girls), and 16 3.5-year-olds (M = 42 months16 days, range = 41;20–43;9; 8 girls) along with their mothers. An additional 12 participants were excluded for the following reasons: did not complete at least two trials of each type (6 2.5-year-olds, 3 3.0-year-olds, and 1 3.5-year-old), mother did not speak English (1 2.5-year-old), and technical problems (1 2.5-year-old). Participants were recruited through a child research participant registry maintained by a university in the midwestern United States. Parents were sent letters detailing the study and later received a follow-up phone call inviting them to participate. Regarding race/ethnicity, 96% of the children were European American and 4% were Asian American. Regarding parental education, 2% of mothers had completed only a high school education, 15% had completed some college education, and 83% had a 4-year college education or beyond. Apparatus and materials The experiment was conducted in a 5.5  11-foot room with a floor to ceiling length curtain that lined the perimeter of the room so as to eliminate additional landmarks. A two-dimensional circular

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landmark (8 in. in diameter) and two identical, completely opaque Plexiglas containers and their lids (3 in. tall, 2.5 in. in diameter) were arranged on the floor (Fig. 1A). A small toy train that fit within the containers served as the hidden object for all trials. Mothers sat in a chair located approximately 48 in. from the edge of the circle. At the beginning of each trial, children sat behind the curtain in a chair to the left of the mother’s chair. Two Sony Handycam DCR-HC96 camcorders were used to record the entire session.

Design and procedure The session started outside of the testing room, where mother–child dyads received instructions about the task. The experimenter instructed the mother to watch where the toy was hidden and to ensure that her child did not watch the hiding event. The experimenter also told the mother to provide her child with enough information so that her child could find the toy on the first try before letting the child search. The mother was instructed not to point but was allowed to continue interacting with her child after providing the first full direction. The experimenter then answered any questions the mother had but refrained from providing any additional instructions and example directions so that the mother’s directions would be as natural as possible. Mother–child dyads then completed two warm-up trials. For these trials, the mother told her child how to find a toy that was hidden in one of two containers. One container was placed on the floor next to a chair approximately 3 feet from where the mother was seated. The other container was located on top of the chair. Both containers were visible at all times, and each container held the toy once during familiarization trials. After the mother watched an experimenter hide a toy, she gave her child directions on how to find the hidden object and then the child searched for the toy. The child was allowed to search until he or she found the object. After completing the warm-up trials, mother–child dyads completed 16 test trials in the testing room. The mother was given the same instructions as in the warm-up trials. At the beginning of every trial, the mother reminded her child to stay hidden behind the curtain so that he or she could not see where the experimenter hid the train. After the hiding event, the mother brought her child out from

Video Camera

Experimenter Video Camera TT1

TT2

TT3

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Mother Child Fig. 1. Diagram (to scale) of testing room (A) and locations of target (darkened for illustration purposes only) and non-target containers in relation to the circle, which served as a landmark (B). TT1/2/3/4, Trial Type 1/2/3/4.

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behind the curtain and gave directions for finding the hidden train. The child was then allowed to search for the object until he or she found it. During each test trial, one container was placed 2 in. from the edge of the circle and the other container was placed 12 in. from the edge of the circle such that both containers were always on the same side of, and at unequal distances from, the landmark. Fig. 1B shows the four trial types used in this experiment (Trial Type 1 [TT1], TT2, TT3, and TT4). Trial types differed in their relative distance to the landmark and the mother–child dyad. In TT1, the target container was located relatively far from the landmark and relatively far from the mother–child dyad. In TT2, the target container was located relatively close to the landmark and relatively close to the mother–child dyad. In TT3, the target container was located relatively close to the landmark and relatively far from the mother–child dyad. In TT4, the target container was located relatively far from the landmark and relatively close to the mother–child dyad. Participants completed four blocks of trials for a total of 16 trials. Each of the four trial types occurred once in each block, and the order of the four trial types was randomized within each block. Two consecutive trials could be the same only if they were from different blocks. Coding and measures Each session was video-recorded and transcribed verbatim for coding. We implemented a coding scheme similar to the one developed by Plumert et al. (2012) that classified the reference frames and spatial terms mothers used most often when communicating about the target location. Consistent with Plumert et al., only directions given before children approached the containers were coded. Reference frames. The overwhelming majority of the reference frames used were landmark, person, and order references. A landmark reference included any reference to the circle, curtain, or back wall of the testing room as well as any implicit reference to an external landmark such as ‘‘the close one” for TT3 when the target container was relatively close to the landmark and far from the mother. A person reference included any reference to ‘‘me” (mother) or ‘‘Mommy,” ‘‘you” (child), and ‘‘us” (mother and child) as well as any implicit reference to the self such as ‘‘the close one” for TT4 when the target container was relatively close to the mother and far from the landmark. We chose to call all of these person references because the mother–child dyad shared the same viewpoint. Finally, an order reference included any reference to the order in which the containers appeared from the perspective of the mother and child (e.g., ‘‘the first one”) or any instance in which the mother numbered the containers such as ‘‘cup number two.” Scores were calculated for each type of reference frame by dividing the total number of times mothers used the reference frame within a trial type by the total number of each trial type completed. This yielded a total of 12 scores that represented the mean number of landmark, person, and order references per trial for each trial type. Spatial relational terms. Mothers predominantly used two spatial relational terms when conveying the location of the hidden toy. The first consisted of variants of close to, including by, near, next to, and not far from. The second consisted of variants of far from, including away from, not by, and not close to. As with reference frames, scores were calculated by dividing the total number of times mothers used either close to or far from terms within a trial type by the total number of each trial type completed. This yielded a total of eight scores that represented the mean number of close to and far from references per trial for each trial type. Trials completed. Trials were excluded from analyses if mothers pointed at the containers, children searched before any directions were given, children opened both containers simultaneously, or children did not complete a trial. An Age (3)  Trial Type (4) repeated-measures analysis of variance (ANOVA) on the number of completed trials of each type revealed a significant effect of age, F(2, 45) = 3.663, p = .034, ɳ2p = .14, indicating that 2.5-year-olds completed fewer trials than 3.5-year-olds (p = .029). The mean numbers of trials completed for 2.5-, 3.0-, and 3.5-year-olds were 3.50 (SD = 0.35), 3.72 (SD = 0.29), and 3.81 (SD = 0.25), respectively. The mean numbers of trials completed for TT1, TT2, TT3, and TT4 were 3.56 (SD = 0.54), 3.73 (SD = 0.54), 3.69 (SD = 0.51), and 3.77 (SD = 0.43), respectively.

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Children’s search success. A correct search was defined as finding the hidden object on the first attempt. If a child approached a container but the mother provided additional information after the approach (e.g., ‘‘No, not that one, the other one”) and then the child changed his or her mind, we coded the first container the child approached as the container searched. This occurred on 2.4% of trials. Intercoder reliabilities. Interrater reliabilities (n = 9) for the continuous variables of the number of landmark, person, and order reference frames and the number of spatial terms mothers used on each trial were calculated using intraclass correlations and were .99 and .99, respectively. Reliability for the categorical variable of search success was calculated using Cohen’s kappa (j = .94). Results Mothers’ reference frame use We compared mothers’ use of the three types of reference frames to determine whether their use of landmark, person, and order references shifted depending on the child’s age and the trial type. (Note that a direct comparison of the three reference frames is possible because mothers were free to use all of them on any given trial.) The mean number of landmark, person, and order references per trial for each trial type was entered into an Age (2.5, 3.0, or 3.5 years)  Reference Frame (landmark, person, or order),  Trial Type (TT1, TT2, TT3, or TT4) repeated-measures ANOVA,1 with the first factor as a between-participants variable and the second and third factors as within-participant variables. This analysis yielded a significant main effect of reference frame, F(1.746, 78.575) = 30.84, p < .0001, ɳ2p = .41, and a significant main effect of trial type, F(2.571, 115.693) = 2.82, p = .05, ɳ2p = .06. These main effects were subsumed under a significant Reference Frame  Trial Type interaction, F(4.711, 61.858), p < .0001, ɳ2p = .51. As shown in Fig. 2, simple effects tests revealed a significant effect of reference frame for TT1, F(2, 90) = 11.77, p < .0001, ɳ2p = .21, for TT2, F(2, 90) = 53.29, p < .0001, ɳ2p = .54, for TT3, F(2, 90) = 70.89, p < .0001, ɳ2p = .61, and for TT4, F(1.671, 75.175) = 37.07, p < .0001, ɳ2p = .45. For TT1, TT2, and TT3, mothers used significantly more landmark references than person and order references; there was no significant difference between the numbers of person and order references for these trial types. When the target was closest to the mother–child dyad (TT4), mothers used significantly more person references than landmark and order references; there was no significant difference between the numbers of landmark and order references for this trial type. Mothers’ spatial relational term use We compared mothers’ use of the two predominant spatial terms to examine whether mothers’ use of close to and far from references shifted depending on age and trial type. The mean numbers of close to and far from references per trial for each trial type were entered into an Age (2.5, 3.0, or 3.5 years)  Spatial Relational Term (close to or far from)  Trial Type (TT1, TT3, or TT4) repeated-measures ANOVA with the first factor as a between-participants variable and the second and third factors as within-participant variables. (Because mothers only used close to terms for TT2, when the target container was close to both the landmark and the dyad, we excluded this trial type from the analysis.) This analysis yielded a significant main effect of age, F(2, 45) = 7.24, p = .002, ɳ2p = .24. Mothers provided more spatial terms to 2.5-year-olds (M = .99, SD = .22) than to both 3.0-year-olds (M = .75, SD = .36) and 3.5-year-olds (M = .64, SD = .16). This analysis also yielded a significant main effect of spatial term, F(1, 45) = 39.56, p < .0001, ɳ2p = .47, which was subsumed under a significant Spatial Term  Trial Type interaction, F(2, 90) = 89.60, p < .0001, ɳ2p = .67. Simple effects tests revealed a significant effect of spatial term for TT1, F(1, 45) = 30.51, p < .0001, ɳ2p = .40, for TT3, F(1, 45) = 119.28, p < .0001, ɳ2p = .73, and for TT4, F(1, 45) = 97.67, p < .0001, ɳ2p = .69. Mothers used close to references significantly more often than far from references when the target container was close to the landmark and far from the mother (TT3: M = 1.30, SD = 0.42 for close to terms and M = 0.27, SD = 0.61 for far from terms) and when it was close to the mother and far from the landmark (TT4: M = 1.31, SD = 0.07 for close to terms and 1

Greenhouse–Geiser corrections were made for all analyses where the assumption of sphericity was violated.

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Fig. 2. Mean numbers of landmark, person, and order references per trial by trial type in Experiment 1. Note that the target container is darkened in this figure for illustration purposes only. Brackets with asterisks represent a significant difference between a pair of means. Error bars depict standard errors. TT1/2/3/4, Trial Type 1/2/3/4.

M = 0.19, SD = 0.08 for far from terms). The only time mothers used far from references significantly more often than close to references was when the target container was relatively far from both the landmark and the dyad (TT1: M = 1.23, SD = 0.60 for far from terms and M = 0.46, SD = 0.62 for close to terms). In this case, use of close to terms was in reference to the curtain or the back wall of the room. Children’s search success The mean proportion of correct searches was entered into an Age (2.5, 3.0, or 3.5 years)  Trial Type (TT1, TT2, TT3, or TT4) repeated-measures ANOVA. There was a significant main effect of age, F(2, 45) = 13.33, p < .0001, ɳ2p = .37, indicating that 3.5-year-olds (M = .95, SD = .08) searched correctly significantly more often than 2.5-year-olds (M = .68, SD = .19) and 3.0-year-olds (M = .83, SD = .15) and that 3.0-year-olds searched correctly significantly more often than 2.5-year-olds. There was also a significant main effect of trial type, F(3, 135) = 3.31, p = .02, ɳ2p = .07, such that children searched correctly more often on TT2 (M = .88, SD = .22), TT3 (M = .88, SD = .24), and TT4 (M = .83, SD = .26) than on TT1 (when the target container was far from both the dyad and the circle; M = .74, SD = .31). We also used separate one-sample t tests for each age group and trial type to compare the proportion of correct searches with the chance value of .50 (Fig. 3). The 3.0- and 3.5-year-olds searched at levels significantly above chance on all trial types, ts(15) > 3.03, p < .009, and ts(15) > 7.34, p < .0001, respectively. The 2.5-year-olds searched at levels significantly above chance for all trial types, ts(15) > 2.27, p = .04, except for TT1 (when the target was far from both the landmark and the dyad), t(15) = 1.00, ns. Contingencies between mothers’ reference frame use and children’s search success We first examined whether the number of reference frames mothers provided predicted children’s search success in the task. Given the significant age differences in search performance, we ran separate logistic regression analyses for each age group, where we used the total number of references mothers provided on a single trial to predict whether children searched correctly. These logistic regression models all were nonsignificant, v2(1) = 1.17, ns, v2(1) = 0.436, ns, and v2(1) = 1.71, ns, for the 2.5-, 3.0-, and 3.5-year-olds, respectively. We were also interested in whether the proportions of trials in which children searched correctly in response to landmark-only reference frames and person-only reference frames exceeded those

M.G. Lorenz, J.M. Plumert / Journal of Experimental Child Psychology 178 (2019) 41–59

TT1

TT2

1 Proportion of correct searches

0.9 0.8

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TT4

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0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2.5 years

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3.5 years

Fig. 3. Proportion of correct searches by age and trial type in Experiment 1. Note that the dashed line represents chance performance. Asterisks represent performance that is significantly above chance. Error bars depict standard errors. TT1/2/3/4, Trial Type 1/2/3/4.

expected by chance (.50). Given that mothers used order-only references on only 3% of trials, we excluded order-only trials from these analyses. We also excluded trials in which mothers used a mixture of landmark, person, and order reference frames or another type of reference frame (26% of trials). Separate one-sample t tests revealed that 2.5-year-olds’ searches were significantly above chance in response to landmark references, t(14) = 2.724, p = .016 (M = .71, SD = .29) but were not significantly different from chance in response to person references, t(13) = 1.893, ns (M = .70, SD = .40). However, 2 2.5-year-olds never searched correctly in response to person references. When excluded from the analyses, the remaining 12 2.5-year-olds were significantly above chance in response to person references, t(11) = 3.81, p = .003. The 3.0-year-olds’ searches were significantly above chance in response to both landmark references, t(14) = 7.34, p < .0001 (M = .84, SD = .18), and person references t(14) = 13.06, p < .0001 (M = .93, SD = .13). Similarly, the 3.5-year-olds’ searches were significantly above chance in response to both landmark references, t(15) = 19.98, p < .0001 (M = .96, SD = .09), and person references, t(14) = 15.58, p < .0001 (M = .94, SD = .11). Discussion These results clearly demonstrate that when the distance between the containers and the circle landmark was small, mothers were quite systematic in their direction-giving and all age groups exhibited strong search performance. In terms of direction-giving, mothers focused on the relative proximity of the target container to the circle except when the target container was relatively close to the mother and far from the circle, when mothers most frequently referenced the dyad. Similarly, mothers were very systematic in their use of spatial terms. Mothers overwhelmingly preferred to use close to for all trial types except TT1, when the target was relatively far from the landmark and the mother–child dyad. In terms of direction-following, the 3.0- and 3.5-year-olds searched at levels significantly above chance on all trial types, and even the 2.5-year-olds searched at levels significantly greater than chance on trial types except for TT1, when the target was relatively far from both the landmark and the dyad. The 3.5-year-olds were significantly more likely to search correctly than both the 2.5- and 3.0-year-olds, and the 3.0-year-olds were significantly more likely to search correctly than the 2.5-year-olds. The contingency analyses revealed that all age groups’ search success was above chance in response to both landmark and person references but that the total number of reference frames did not predict search success for any age group. This suggests that children’s search success depended on the type, and not the number, of reference frames provided. Interestingly, the 2.5-year-olds performed better in this experiment than they did in the Plumert et al. (2012) study. This indicates that it is easier for children to make comparisons of the relative

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proximity of two objects to a single landmark than to two landmarks. The only trial type that resulted in chance performance was when the target was relatively far from both the landmark and the dyad. The 2.5-year-olds may have struggled on this trial type because they had difficulty in inhibiting searching the first container they reached, although this is likely not the case given that they were successful on TT3, where they needed to bypass the non-target container before reaching the target container. Instead, it is much more likely that the 2.5-year-olds had difficulty in following directions because they frequently included far from references, which are unusual in the context of everyday direction-giving and direction-following. This explanation would also be consistent with the results of Plumert et al.’s second experiment, which demonstrated that young children have great difficulty in following directions that incorporate the relation far from. Mothers’ systematic reference frame use when giving directions coupled with children’s strong search performance suggests that the small absolute distance between the containers and the landmark positively affected performance in this task. Thus, we conducted a second experiment to examine how increasing the absolute distance between the two containers and the landmark would affect both mothers’ direction-giving and children’s subsequent direction-following. We hypothesized that the increased absolute distance would negatively affect children’s search success, which would be consistent with the previous finding that young children have more difficulty in making judgments of nearby-ness when absolute distance is increased (Hund & Plumert, 2007). We also hypothesized that mothers would attempt to compensate for children’s difficulty with the increased absolute distance by providing more information (i.e., a greater number of reference frames) in their directions. Experiment 2 Method Participants A total of 48 mother–child dyads participated, with approximately equal numbers of boys and girls in each age group. There were 16 2.5-year-olds (M = 30 months 5 days, range = 29;17–31;5; 8 girls), 16 3.0-year-olds (M = 36 months 16 days, range = 35;13–37;29; 9 girls), and 16 3.5-year-olds (M = 42 months 17 days, range = 41;17–43;12; 8 girls) along with their mothers. An additional 22 participants were not included for the following reasons: did not complete at least two trials of each trial type (13 2.5-year-olds, 3 3.0-year-olds, and 1 3.5-year-old), English was the child’s second language (1 child), technical problems (3 children), and sibling was in the room (1 child). Participants were recruited in the same manner as Experiment 1. Regarding race/ethnicity, 96% of the children were European American, 2% were Hispanic/Latino, and 2% were Asian American. Regarding parental education, 20% of mothers had completed some college education and 80% of mothers had a 4-yearcollege education or beyond. Apparatus and materials The apparatus and materials were the same as those used in Experiment 1. Design and procedure All aspects of the design and procedure were the same as in Experiment 1 with the exception of the placement of the containers. For each test trial, one container was placed 12 in. from the edge of the circle and the other container was placed 22 in. from the edge of the circle. An Age (3)  Trial Type (4) repeated-measures ANOVA on the number of trials of each type completed yielded no significant effects. The mean numbers of trials completed for TT1, TT2, TT3, and TT4 were 3.42 (SD = 0.74), 3.42 (SD = 0.74), 3.50 (SD = 0.58), and 3.50 (SD = 0.62), respectively. Coding and measures The coding and measures were identical to those used in Experiment 1. On 7.1% of trials, we coded the first container approached as the container searched. Interrater reliabilities (n = 9) on the number of landmark, person, and order reference frames (.99) and the number of spatial terms mothers used

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on each trial (.99) were calculated using intraclass correlations. Reliability for the categorical variable of search success was calculated using Cohen’s kappa (j = .94). Results Mothers’ reference frame use We compared mothers’ use of landmark, person, and order reference frames to determine whether their use of reference frames shifted depending on the child’s age and the trial type. This analysis yielded a significant main effect of trial type, F(3, 135) = 3.79, p = .012, ɳ2p = .08, which was subsumed under a significant Trial Type  Reference Frame interaction, F(4.52, 203.398) = 27.94, p < .0001, ɳ2p = .38. As shown in Fig. 4, simple effects tests revealed a significant effect of reference frame for TT3, F(2, 90) = 5.77, p = .004, ɳ2p = .11, and for TT4, F(1.338, 60.215) = 47.534, p < .0001, ɳ2p = .51, but no significant effect of reference frame for TT1, F(2, 90) = 1.81, ns, or for TT2, F(2, 90) = 1.41, ns. For TT3, when the target container was relatively close to the landmark and far from the dyad, mothers used significantly more landmark references than person and order references, but there was no significant difference between the numbers of person and order references. For TT4, when the target container was relatively far from the landmark and close to the dyad, mothers used significantly more person references than landmark and order references and used significantly more order references than landmark references. Mothers’ spatial relational term use We again examined whether mothers’ use of close to and far from references shifted depending on age and trial type. (Again, because mothers only ‘‘close to” only for TT2, when the target container was relatively close to both the landmark and the dyad, we excluded this trial type from the analysis.) This analysis yielded a significant main effect of spatial term, F(1, 45) = 11.81, p = .001, ɳ2p = .21, and a significant Spatial Term  Trial Type interaction, F(2, 90) = 71.42, p < .0001, ɳ2p = .61. As expected, mothers used far from references significantly more often than close to references when the target container

Mean number of references per trial

Landmark References

Person References

Order References

*

1.8 1.6

*

1.4

1.2 1 0.8 0.6 0.4 0.2 0 TT1

TT2

TT3

TT4

Fig. 4. Mean numbers of landmark, person, and order references per trial by trial type in Experiment 2. Note that the target container is darkened in this figure for illustration purposes only. Brackets with asterisks represent a significant difference between a pair of means. Error bars depict standard errors. TT1/2/3/4, Trial Type 1/2/3/4.

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was relatively far from both the landmark and the mother (TT1: M = 1.19, SD = 0.70 for far from terms and M = 0.39, SD = 0.67 for close to terms), F(1, 45) = 32.78, p < .0001, ɳ2p = .42. Mothers used close to references significantly more often than far from references when the target container was relatively close to the landmark and far from the mother (TT3: M = 1.09, SD = 0.59 for close to terms and M = 0.72, SD = 0.77 for far from terms), F(1, 45) = 6.52, p = .014, ɳ2p = .13, and when the target container was relatively close to the mother and far from the landmark (TT4: M = 1.41, SD = 0.74 for close to terms and M = 0.08, SD = 0.28 for far from terms), F(1, 45) = 128.62, p < .0001, ɳ2p = .74. Children’s search success We again examined whether the magnitude of correct searches differed by age or trial type. There was a significant main effect of age, F(2, 45) = 16.60, p < .0001, ɳ2p = .43, indicating that 3.5-year-olds (M = .83, SD = .15) searched correctly significantly more often than 2.5-year-olds (M = .51, SD = .15) and 3.0-year-olds (M = .70, SD = .17) and that 3.0-year-olds were significantly more likely to search correctly than 2.5-year-olds. Separate one-sample t tests revealed that the 3.5-year-olds again searched at levels significantly above chance on all trial types, ts(15) > 4.42, p < .0001 (Fig. 5). The 3.0-year-olds also searched at levels significantly above chance for all trial types, ts(15) > 2.48, p < .026, except for TT1, when the target container was relatively far from both the landmark and the dyad, t(15) = 0.66, ns. Unlike Experiment 1, the 2.5-year-olds did not search at levels that differed significantly from chance for any trial type. Contingencies between mothers’ reference frame use and children’s search success We again examined whether the number of reference frames mothers provided predicted children’s search success. As in Experiment 1, these separate logistic regression analyses for each age group all were nonsignificant, v2(1) = 0.62, ns, v2(1) = 0.24, ns, and v2(1) = 0.003, ns, for the 2.5-, 3.0-, and 3.5-year-olds, respectively. We also examined whether the proportion of correct searches exceeded that expected by chance in response to mothers’ use of particular reference frames. We excluded trials in which mothers used a mixture of landmark, person, and order reference frames or another type of reference frame (40% of trials). Separate one-sample t tests revealed that the 2.5-year-olds’ search performance was not significantly different from chance in response to landmark references, t(12) = 0.54, ns (M = .56, SD = .36), person references, t(11) = 0.75, ns (M = .58, SD = .35), or order references, t(8) = 1.77, ns (M = .32, SD = .31). Similarly, the 3.0-year-olds’ search performance did not significantly differ from chance in response to landmark references, t(14) = 0.45, ns (M = .54, SD = .36), or order references, t(6) = 0.37, ns (M = .44, SD = .41), but their searches were significantly above chance in response to person refer-

TT1

TT2

TT3

TT4

Proportion of correct searches

1

*

0.9

* *

0.8

* *

*

*

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2.5 years

3.0 years

3.5 years

Fig. 5. Proportion of correct searches by age and trial type in Experiment 2. Note that the dashed line represents chance performance. Asterisks represent performance that is significantly above chance. Error bars depict standard errors. TT1/2/3/4, Trial Type 1/2/3/4.

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ences, t(12) = 4.42, p = .001 (M = .85, SD = .29). Finally, the 3.5-year-olds’ search performance did not significantly differ from chance in response to order references, t(6) = 0.39, ns (M = .56, SD = .43), but their searches were significantly above chance in response to landmark references, t(10) = 5.51, p < .001 (M = .85, SD = .21), and person references, t(11) = 2.36, p = .04 (M = .72, SD = .33). Cross-experiment comparisons We also conducted a parallel set of cross-experiment ANOVAs on reference frames, spatial terms, and search success with experiment (1 or 2) as an additional factor. This allowed us to directly test how a smaller (Experiment 1) versus larger (Experiment 2) absolute distance between the pair of containers and the landmark affected mother–child communication about relative proximity. To avoid redundancy, only significant effects involving experiment are reported below. The analyses of reference frames revealed a significant effect of experiment, F(1, 90) = 10.23, p < .01, ɳ2p = .10, indicating that, as expected, mothers used significantly more reference frames when the distance between the containers and the landmark was larger (Experiment 2; M = .79, SD = .76) than when the distance was smaller (Experiment 1; M = .62, SD = .74). There was also a significant Experiment  Reference Frame interaction, F(1.832, 164.894) = 13.47, p < .0001, ɳ2p = .13. Mothers used more landmark references in Experiment 1 (M = .95, SD = .72) than in Experiment 2 (M = .73, SD = .74), F(1, 90) = 6.09, p = .016, ɳ2p = .06, whereas they used more person and order references in Experiment 2 (M = .83, SD = .77 and M = .80, SD = .77) than in Experiment 1 (M = .60, SD = .72 and M = .30, SD = .62), F (1, 90) = 6.89, p = .01, ɳ2p = .071 and F(1, 90) = 19.68, p < .0001, ɳ2p = .18, respectively. The analyses of spatial terms revealed a significant Experiment  Age interaction for spatial terms, F(2, 90) = 4.04, p = .021, ɳ2p = .08, indicating that mothers used more spatial terms for 2.5-year-olds when the distance between the containers and the landmark was smaller (Experiment 1; M = .99, SD = .22) than when the distance was larger (Experiment 2; M = .75, SD = .36), F(1, 30) = 5.11, p = .031, ɳ2p = .15. This is likely due to the fact that mothers frequently referred to the order of containers in Experiment 2, which did not include a spatial term. There was also a significant Experiment  Spatial Term  Trial Type interaction, F(2, 180) = 7.08, p < .01, ɳ2p = .07. This interaction was driven by the fact that mothers used significantly more far from terms in Experiment 2 (M = 0.72, SD = 0.77) than in Experiment 1 (M = 0.27, SD = 0.61) when the target container was close to the landmark and far from the dyad (TT3), F(1.831, 164.804) = 7.03, p < .01, ɳ2p = .072. This is consistent with the relatively high number of person references for TT3 in Experiment 2. Finally, cross-experiment analyses of search success revealed that overall children searched significantly less successfully when the distance between the containers and the landmark was larger (Experiment 2; M = .68, SD = .33) than when the distance was smaller (Experiment 1; M = .82, SD = .26), F(1, 90) = 20.41, p < .0001, ɳ2p = .19. Discussion These results are consistent with our hypothesis that increasing the absolute distance between the containers and the landmark would affect both mothers’ direction-giving and children’s directionfollowing. Unlike Experiment 1, mothers frequently used multiple strategies to convey the location of the target container to their children, including a high number of order references. When the target container was relatively far from both the landmark and the dyad (TT1) and when the target container was relatively close to both the landmark and the dyad (TT2), mothers did not significantly differ in their use of landmark, person, and order references, using all three relatively frequently. However, mothers used more targeted strategies on Trial Types 3 and 4, where they preferred whatever was closest to the target location—the landmark for TT3 and the dyad for TT4. Mothers again showed a clear preference for proximity terms, preferring to use close to for all trial types except when the target location was far from both the landmark and them (TT1). The cross-experiment analyses clearly showed that mothers used more reference frames when the distance between the containers and landmark was larger, suggesting that mothers may have used a ‘‘kitchen sink” approach in an attempt to compensate for young children’s difficulty with the increased distance. Increasing the absolute distance between the containers and the circle also negatively affected children’s search success. Cross-experiment analyses revealed that children successfully searched

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significantly less often in Experiment 2 compared with Experiment 1. This result is especially salient for the 2.5-year-olds. In contrast to Experiment 1, the 2.5-year-olds never searched at levels that significantly differed from chance for any trial type. Furthermore, an additional 13 2.5-year-olds did not complete at least two trials of each trial type (and therefore were excluded from the experiment), indicating that the task was particularly difficult for the youngest age group. The contingency analyses similarly demonstrated developmental differences in young children’s ability to use different reference frames to guide their searches. The 2.5-year-olds did not search successfully in response to landmark or person references, whereas the 3.0-year-olds searched successfully in response to person references and the 3.5-year-olds searched successfully in response to both landmark and person references. Notably, children across the three age groups never searched at a level above chance in response to order references, and just as in Experiment 1, the total number of references provided on a given trial did not predict search success for any age group. Although increasing the distance between the containers and the landmark led to a clear impairment in 2.5-year-olds’ search success, the source of the impairment remains unclear. Did the youngest children have a hard time in identifying the target container because the absolute distance was greater or because of mothers’ less systematic directions? To identify why 2.5-year-olds struggled to search successfully in Experiment 2, we conducted a third experiment where we maintained the larger absolute distance but controlled the reference frame mothers used on a given trial. Because 2.5-year-olds performed significantly above chance in Experiment 1, we used mothers’ predominant reference frames in Experiment 1 as the model for reference frame use in Experiment 3. As such, mothers were instructed to use a landmark frame of reference for TT1, TT2, and TT3 and to use a person frame of reference for TT4. Any difference in 2.5-year-olds’ search performance across Experiments 2 and 3 would indicate an effect of the increased distance between the containers and the landmark. Experiment 3 Method Participants A total of 16 2.5-year-olds (M = 30 months 28 days, range = 29;10–33;12; 7 girls) and their parents participated (15 were mothers and 1 was a father2), with approximately equal boy and girl participants. Participants were recruited in the same manner as Experiments 1 and 2. Data from 3 additional participants were excluded because they did not complete at least two of each trial type. Regarding race/ethnicity, 68% of the children were European American, 5% were American Indian, and 16% were multiracial. Regarding parental education, 16% of mothers had completed some college education and 73% had a 4year college education or beyond (11% did not provide demographic information). Apparatus and materials The apparatus and materials were the same as those used in Experiments 1 and 2 except that the toy train was replaced with a small toy puffer fish. Design and procedure All aspects of the design and procedure were the same as in Experiment 2 with the exception of the instructions to the mothers. During the two familiarization trials outside of the testing room, the experimenter instructed the mother to tell her child once where the toy was in relation to the circle and once where it was in relation to herself. During the 16 test trials, the experimenter told the mother which reference frame to use on a given trial. After the dyad was settled in the testing room, the experimenter said, ‘‘I’ll hide the fish in one of these containers while [child’s name] is behind the curtain. Then you’ll tell [child’s name] where the fish is in relation to [the circle, yourself], just as we did during the practice trials.” Mothers were instructed to refer to the circle for TT1 (far from both the landmark 2 The father who participated was the primary caregiver. Of the 112 families who participated in our final sample, he was the only father, which is why we chose to use ‘‘mother” when interpreting our results throughout the article.

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and the dyad), for TT2 (close to both the landmark and the dyad), and for TT3 (close to the landmark and far from the dyad) and to refer to themselves for TT4 (far from the landmark and close to the dyad) to align with the pattern of reference frame use seen in Experiment 1. The experimenter reminded them of the reference frame to use at the beginning of every trial. Mothers accurately followed the experimenter’s instructions on the vast majority of trials, using the correct reference frame on 96% of trials. The remaining 4% of trials in which mothers did not adhere to the protocol and provided incorrect or multiple reference frames were excluded from the analyses below. A one-way repeated-measures ANOVA on the number of trials of each type completed yielded no significant effects. The mean numbers of trials completed for TT1, TT2, TT3, and TT4 were 3.19 (SD = 0.83), 3.44 (SD = 0.73), 3.38 (SD = 0.81), and 3.75 (SD = 0.58), respectively. Coding and measures The coding and measures were identical to those used in Experiments 1 and 2. On 8.6% of trials, we coded the first container approached as the container searched. Reliability for the categorical variable of search success was calculated using Cohen’s kappa (j = 1.00). Results and discussion We tested whether 2.5-year-olds’ search performance differed across trial types and was above chance on any trial type. A repeated-measures ANOVA with trial type as a within-participant factor was not significant, F(3, 45) = 0.07, ns, suggesting that there was no difference in search success across trial types. Likewise, separate one-sample t tests revealed that children were not above chance (.50) on any of the trial types, ts(15) < .30, ns. The mean proportions correct for TT1, TT2, TT3, and TT4 were .52 (SD = .27), .55 (SD = .36), .51 (SD = .30), and .56 (SD = .40), respectively. A cross-experiment comparison of search success in Experiment 2 (M = .51, SD = .15) and Experiment 3 (M = .54, SD = .10) was not significant, F(1, 30) = 0.43, ns. These results indicate that the decline in 2.5-year-olds’ search success from Experiment 1 to Experiment 2 was driven by the increase in absolute distance and not mothers’ direction-giving. Even though mothers’ directions were the same as those that 2.5-year-olds successfully followed in Experiment 1, 2.5-year-olds in Experiment 3 failed to search at levels significantly above chance on all trial types. These results suggest that young children may have trouble in following directions involving relative proximity in less prototypical cases (i.e., larger distances), a point we discuss further in the General Discussion.

General discussion The current investigation examined how altering the absolute distance between a pair of hiding locations and a landmark affected mother–child communication about relative proximity. Even though the relative proximity of the two containers to the landmark did not change, just moving the pair 10 in. farther from the landmark was enough to perturb both mothers’ direction-giving and young children’s direction-following. In terms of mothers’ direction-giving, they seemed to employ a kitchen sink strategy in which they included multiple frames of reference (landmark, person, and order) in their directions. This stands in contrast to mothers’ direction-giving in Experiment 1. Mothers typically referred to a single frame of reference in their directions and almost never referred to the order of the two containers. In terms of search success, children clearly performed significantly better in Experiment 1 than in Experiment 2. The impact of the absolute distance between the pair of containers and the landmark was greatest for the youngest age group, with 2.5-year-olds’ search success not being above chance for any trial types in Experiment 2 but being above chance for all trial types in Experiment 1 except for TT1, when the target container was far from both the landmark and the dyad. Experiment 3 confirmed that the increased absolute distance, and not the mothers’ direction-giving style, resulted in 2.5-year-olds’ impaired search performance in Experiment 2. These results are remarkably consistent with those of Hund and Plumert (2007) and Hund and Naroleski

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(2008), which showed that increasing the absolute distance of objects to a landmark impaired young children’s ability to judge and remember the relative proximity of those objects to the landmark. What might account for this pattern of results? Like previous research on young children’s understanding of dimensional adjectives (Clark, 1970; Sera & Smith, 1987; Smith et al., 1986, 1988), it appears that young children’s understanding of relative proximity is initially restricted to prototypical cases of relative proximity to a landmark. When children heard directions with ‘‘close” and saw a highly prototypical case of relative closeness (i.e., the target container was only 2 in. from the circle), children of all ages searched successfully. However, when children heard directions with ‘‘close” and saw a much less typical case of relative closeness (i.e., the target was 12 in. from the circle), 2.5-yearolds no longer searched successfully above chance. These results suggest that young children’s initial understanding of relative proximity is restricted to prototypical cases. With development, young children’s understanding of relative proximity includes a greater range of distances. A critical component of this development is the understanding that the absolute distance between a pair of locations and a landmark is irrelevant for comparisons of relative proximity. For example, we would judge one person as closer than another person to a checkout register regardless of whether the two people were near the beginning or the end of the checkout line. Such an understanding is important for flexibly communicating about relative location across a range of contexts. Whether indicating which runner is closer to the finish line of a race or indicating that New York City is closer to Chicago than to San Francisco, both contexts involve the same underlying understanding of how to make comparisons of relative proximity. Currently, it is not known whether children gradually incorporate larger absolute distances into their judgments of relative proximity or whether they undergo a distinctive shift in the understanding of relative proximity (i.e., understanding that absolute distance is irrelevant). Further research is needed to determine the limits of older children’s understanding of relative proximity, particularly in large-scale contexts. These results also show that the spatial configuration of the two containers and the landmark plays a critical role in communication about relative proximity. In both Experiment 1 and Plumert et al. (2012), the target and non-target containers were always 2 and 12 in. away from the landmark. However, they were placed on opposite sides of the landmark in Plumert et al. and on the same side of the landmark in Experiment 1. Unlike Plumert et al., mothers in the current investigation often used comparative suffixes (e.g., ‘‘the closer one,” ‘‘the closest one”) to convey more information about the relative proximity of the target and non-target containers to the landmark. Overall, use of comparative suffixes was high across experiments, with mothers typically including comparative suffixes on every trial (M = 1.21 per trial, SD = 0.90 for Experiment 1 and M = 1.05 per trial, SD = 0.72 for Experiment 2). Mothers’ use of these terms in the current experiments supports the notion that the organization of the spatial array itself invited mothers to view the canisters in terms of their relative proximity (i.e., closer vs. farther) to a single landmark. Mothers also employed an entirely novel strategy to describe the target location in the current investigation—referring to the order of the two containers. Most frequently, this involved providing children with ordinal labels for the containers (e.g., ‘‘It’s in the first container”). Cross-experiment analyses revealed that mothers used this strategy much more often in Experiment 2 than in Experiment 1, suggesting that this strategy resulted from an interaction between the configuration of the spatial array and the larger absolute distance. However, none of the age groups benefitted from ordinal frames of reference, with even the 3.5-year-olds not searching above chance in response to ordinal references. What might account for young children’s difficulty with ordinal references? Although children as young as 3 years understand how to count to three (Carey, 1998; Fuson, 1988; Wynn, 1990), the ability to understand and use ordinal labels develops later during the preschool years (Gentner & Christie, 2006; Miller, Marcovitch, Boseovski, & Lewkowicz, 2015). Young children may have found ordinal references challenging because they involved an implied spatial frame of reference. In the current investigation, mothers never explicitly included a spatial frame of reference with the ordinal label (e.g., ‘‘It’s in the first one relative to us”), likely because the mother and child shared the same perspective. This missing information may have prevented children from correctly interpreting the ordinal references in this task. Young children may also have found ordinal references challenging because they required an

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understanding of the mapping between an abstract number system and the physical containers in the array, whereas circle and person references more simply required children to identify the physical entity to which their mothers were referring. Either or both of these possibilities may account for children’s difficulty in using ordinal information to guide their searches. At a more general level, what do these results suggest about mothers’ sensitivity to young children’s direction-following skills? On the one hand, mothers seemed to recognize that young children would have difficulty when the absolute distance was larger, as evidenced by mothers frequently using multiple types of reference frames and using more reference frames overall in Experiment 2 (the kitchen sink strategy). On the other hand, children did not benefit from mothers’ use of more reference frames or from their use of ordinal references. In fact, 2.5-year-olds’ especially poor performance in Experiment 2 when the target was close to the dyad and far from the circle (TT4) might have been due to the high number of order references mothers provided on this trial type. Nor did children benefit from mothers’ prompts to stay on task (e.g., ‘‘Listen to Mommy!”, ‘‘Wait!”, ‘‘Don’t go yet!”). Specifically, additional coding yielded no significant correlations between the proportion of prompted trials and the proportion of successful searches in any of the experiments. These results suggest that mothers are sensitive to children’s direction-following skills but that they might not always know how to best support their children in challenging tasks (especially when they are not allowed to use other strategies such as pointing). One open question these findings raise is to what extent children’s performance in the current task depends on their linguistic abilities. Indeed, to reliably search correctly in the communication task used here, children needed to comprehend proximity terms such as close and far. However, it is unknown how young children code relative proximity for themselves in a memory task. Young children may rely solely on a visual coding strategy, as some animal species are known to do (Cheng, 1989; Jones, Antoniadis, Shettleworth, & Kamil, 2002; Kamil & Jones, 1997, 2000; Spetch, Rust, Kamil, & Jones, 2003), or they may use a verbal coding strategy (e.g., remembering that the toy is hidden in the closer container). There is also the possibility that young children may be able to visually code relative proximity before reliably comprehending or producing close/far but that having a better understanding of these terms leads to stronger memory for the relative proximity of a target and non-target location to a landmark. Future work will need to untangle these possibilities so as to better understand the specific role that language plays in understanding relative proximity. With the recent increased interest in how communication between mothers and children facilitates spatial development (Ferrara, Hirsh-Pasek, Newcombe, Golinkoff, & Shallcross Lam, 2011; Pruden, Levine, & Huttenlocher, 2011; Szechter & Liben, 2004; Zosh et al., 2015), the current results contribute to the literature by demonstrating that subtle shifts in absolute distance and spatial configuration lead to large shifts in mothers’ direction-giving and children’s direction-following. These findings are also noteworthy because they are the first to show that children as young as 2.5 years are able to successfully follow directions involving an external landmark frame of reference. One limitation of the current work is the similarity in mothers’ education level, cultural background, and socioeconomic status. As such, we caution about the generalizability of the results because there are known differences in how mothers from different socioeconomic backgrounds communicate with their children (Hart & Risley, 1995) as well as cultural differences in the reference frames used to communicate about different spatial locations (Haun, Rapold, Janzen, & Levinson, 2011). Thus, future research will need to address the generalizability of the current results in addition to determining the specific role of language in children’s understanding of relative proximity. Acknowledgments This work was supported by a grant from the National Science Foundation (BCS-0343034) and a Starch Faculty Fellowship awarded to Jodie M. Plumert. The authors thank the parents and children who participated in these studies. We also thank Kathryn Haggerty, Andrew Mickunas, Ashley Buksa, Hanxi Tang, and Nora Tucker for their help in collecting and coding the data and thank Elizabeth O’Neal for assistance with data analysis.

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